Recovering unknown source function for composite fractional relaxation equations (Letters in Nonlinear Analysis and its Applications, 2025)
A backward problem for composite fractional relaxation equations is considered with the Caputo fractional derivative. Based on a spectral problem, the representation of solutions is established. Next, we show the mildly ill-posedness in the Hadamard sense. After that, we show the regularization solution using two regularization methods : the Landweber regularization method and the iterative method. Then, the convergence rate between the exact solution and the regularized solution is provided, under the a priori parameter choice rule.
Keywords: Inverse source problem; regularization method.; Caputo fractional derivative; diffusion-wave equation; ill-posed problem